Solve the following systems of equations:

`x/7 + y/3 = 5`

`x/2 - y/9 = 6`

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#### Solution

The given system of equation is

`x/7 + y/3 = 5` ...(i)

`x/2 - y/9 = 6`.....(ii)

From (i), we get

`=> (3x + 7y)/21 = 5`

`=> 3x + 7x = 105`

`=> 3x = 1.5 - 7y`

`=> x = (105 - 7y)/3`

From (ii), we get

`(9x - 2y)/18 = 6`

=> 9x - 2y = 108......(iii)'

Substituting x = `(105 - 7y)/3` in (iii) we get

`9(105 - 7y)/3 - 2u = 108`

`=> (948 - 63y)/3 - 2y = 108`

=> 945 - 63y - 6y = 108 x 3

=> 945 - 69y = 324

`=> 945 - 324 = 69y`

=> 69y = 621

=> y = 621/69 = 9

Putting y = 9in x = `(1105 - 7y)/3` we get

`x = (105 - 7 xx 9)/3 = (105 - 63)/3`

`= x = 42/3 = 14`

Hence, the solution of thee given system of equations is x = 14, y = 9

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method

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